Given information:
- We are given an arithmetic progression (AP).
- The ratio of the product of the extremes (first term and fourth term) to the product of the means (second term and third term) is 5:6.
- The sum of the terms in the AP is 56.

Let's solve the problem step by step:

Step 1: Finding the common difference (d) of the AP:
- In an AP, the difference between any two consecutive terms is constant, called the common difference (d).
- Let's assume the first term of the AP is 'a', and the common difference is 'd'.

Step 2: Expressing the terms of the AP:
- The first term of the AP is 'a'.
- The second term of the AP is 'a + d'.
- The third term of the AP is 'a + 2d'.
- The fourth term of the AP is 'a + 3d'.

Step 3: Forming an equation using the given information:
- According to the given information, the ratio of the product of the extremes to the product of the means is 5:6.
- The product of the extremes (first term and fourth term) is (a) * (a + 3d).
- The product of the means (second term and third term) is (a + d) * (a + 2d).
- So, we can form the equation: (a) * (a + 3d) / (a + d) * (a + 2d) = 5/6.

Step 4: Simplifying the equation:
- Cross-multiplying the equation, we get: 6 * (a) * (a + 3d) = 5 * (a + d) * (a + 2d).
- Expanding both sides of the equation, we get: 6a^2 + 18ad = 5a^2 + 15ad + 10ad + 30d^2.
- Simplifying further, we get: a^2 - 13ad - 30d^2 = 0.

Step 5: Solving the equation:
- Since we have a quadratic equation, we can solve it using factorization or the quadratic formula.
- Factoring the equation, we get: (a - 15d)(a + 2d) = 0.
- Therefore, either (a - 15d) = 0 or (a + 2d) = 0.
- If (a - 15d) = 0, then a = 15d.
- If (a + 2d) = 0, then a = -2d.

Step 6: Finding the values of a and d:
- Since the sum of the terms in the AP is 56, we can form the equation: a + (a + d) + (a + 2d) + (a + 3d) = 56.
- Substituting the values of a and d from the previous steps, we get: 15d + (15d + d) + (15d + 2d) + (15d +